In applications of robots such as a sealing robot or an arc welding robot, for example, when bringing the robot to continuously make rectilinear motion or arcuate motion, it is often necessary that motion paths be connected with a smooth connecting curve and that velocity control be performed for the robot motion along the connected curve. There have already been made several proposals for the curve to connect the paths of uniform rectilinear motions accompanying the velocity control of the motion on such a connecting curve. However, there has not been any interpolation method by which a smooth velocity control can be realized in those cases where one or both of motions to be connected are arcuate motions, in which the acceleration cannot be zero (nonzero-acceleration motion), so that the velocity control of such motions has been given up. This has been a major hindrance to the construction of the system for control or teaching of the robot.